Answer: About 30 years
Explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 10000
r = 8% = 8/100 = 0.08
n = 1 because it was compounded once in a year.
A = 100000
Therefore,
100000 = 10000(1+0.08/1)^1 × t
100000/10000 = (1.08)^t
10 = (1.08)^t
Taking log to base 10 of both sides, it becomes
Log 10 = log 1.08^t
1 = t × log 1.08 = 0.03342t
t = 1/0.03342
t = 29.9
Approximately 30 years